Not a whole lot. The Outside design is a bit different between the 2, some of the D600's actually had better screen resolution over most of the D610 series, The processor speeds were fairly close 1.6ghz-2.2ghz, The motherboards were different ( D610 being more upgraded) The D600 Takes DDR Ram and the D610 Takes DDR2 Ram.
The D600 was a bit lighter in weight, the D610 a bit on the heavy side.